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By Robert O. Davis, Phillip A. Abbott

The response of geologic materials subject to nuclear weapon effects is of considerable interest in the design of buried protective construction. Recently, more consideration has been given to placing such structures in rock rather than in soil. Although rock has the obvious advantages of high strength and low deformability, discontinuities such as joints and fault planes severely complicate any response analysis. Nevertheless, some knowledge of the effects of these discontinuities must be developed, even if that knowledge remains largely qualitative in nature. In this paper, we present a constitutive description of cracked rock subject to uniaxial shock loading. The constitutive equations are based on certain average response characteristics of a particular cracked rock model. Rather than attempt to represent each material discontinuity individually, we have incorporated the discontinuity effects into constitutive relationships for a continuous medium. The resulting equations are suitable for use in hydrodynamic computer codes presently used for ground motion calculations. APPROACH The continuum description which will be presented below is based on a detailed analysis of a particular cracked rock model. This model can be visualized as a sequence of plates (representing the intact rock) separated by gaps (representing the discontinuities). This so-called "plate-gap" model was first used by Thouvenin (1) in an effort to explain the behavior of porous materials at high

Jan 1, 1971

By A. L. Mular

Several capital cost estimation procedures are reviewed briefly, although the factored estimate method is discussed in preference. A table of cost versus equipment parameter data is provided, where the cost may be updated from the current value of the M&S cost index for mining and milling. Cost equations are useful to prepare computer programs which perform capital cost calculations. The use of the factored estimate method is illustrated.

Jan 1, 1978

By E. L. Corp, J. C. Johnson, W. G. Pariseau, M. Poad, M. E. Fowler

This paper describes a comprehensive geomechanics case study of a full¬scale test stope at the Carr Fork Mine. The mine is owned by Anaconda Miner¬als Company and is located near Tooele, Utah. Large diameter blast holes were used in a new method known as blast hole post-fill (BHPF). The new design proved highly successful in contrast with earlier experience with vertical crater retreat (VCR) stopes. The main geomechanics objective was the estab¬lishment of a design procedure for optimizing stope and pillar dimensions with respect to productivity and recovery. An integrated three-part approach consisting of mine measurements, laboratory testing and finite element calcu¬lations was taken. Independent correlations of 0.88 and 0.89 between calculated and measured displacements and between estimated and observed yield :ones substantiate the finite element design approach using UTAH-II. Subse¬quent stope and pillar design analyses indicate that doubling of the original stope width at 50% extraction is quite possible without sacrifice of safety or stability.

Jan 1, 1984

By Y. C. Liu

THE existence of mechanical twins in bcc metals has long been known. With recent intensive interest in the mechanism of twin formation and its role in plasticity and crack initiation, a study of the general Characteristics of twin intersection appears pertinent. The scope of the present note will be limited to the crystallography of the twin intersections of (112) twins, without consideration of its mechanism, movement of atoms, crystal structure, or the strain energy involved at such an intersection. The twinning elements of (112) twins are considered to be K1 = {112}, n1 = (111) and K2 = {112}, n2 = (111) with a twin shear of 0.707. The crystallographic features of twin intersections have been worked out in detail by Cahn.1 The present work applies the general principles postulated by Cahn to the intersections of (112) twins. The basic conditions for the twin intersection are: 1) The trace of crossing (A) and the secondary (C) twins in the planes of the crossed twin (B) must be parallel. 2) The direction (n1) and magnitude (s) of shear must be identical in the crossing and secondary twins. Also the sense of shear must be the same. These two conditions have to be fulfilled in order to maintain geometrical continuity at the twin interfaces. Fig. 1 shows the perspective representation of how these two conditions are fulfilled at the intersection. This type of intersection will be named Type-I. It is the purpose of this note to point out the existence of another type of intersection, Type-II, as shown in Fig. 2. In this type of intersection, the crossing twin A remains straight and the crossed twin B has been bent. The two conditions laid down by Cahn must also be met. This leads to the following corollary conditions: 1) The interface between twins B and C must be parallel to the twin habit of crossing twin A. 2) n1c must be parallel to n1A. 3) The twin shear (s) of twin C must be exactly equal to and in the same sense as that of crossing twin A. Thus, in order for the Type-II intersection to take place, the twining elements of secondary twin C must fulfill the above three conditions with respect to crossing twin A. Let K1 of crossed twin B be (112). All indices of the matrix can therefore be converted into new in-

Jan 1, 1963

By Charles Meyer, Reno H. Sales

AT Butte, successive zones of sericitized and argillized quartz monzonite occur around every ore-bearing fracture regardless of its size, attitude, or relative age. The two types of alteration always occupy the same relative positions; sericite adjacent to the ore-bearing vein, clay minerals always between the sericitized rock and fresh quartz monzonite, except where overlap of alteration effects between adjacent fissures has eliminated the lower grade mineralogical products, as is the case in much of Butte's Central zone of pervasive sericitization. As long as active circulation continued in the channel, each zone migrated away from the fissure, that is, it grew at its outer edge and simultaneously receded at its veinward edge because of encroachment by the next innermost zone. The different mineralogical and chemical responses within the wall rocks to the attack by the ore fluid are dependent not on a drastic about-face change of composition of the fluid in the channel relative to its ability to alter the quartz monzonite but on continuously varying conditions of physico-chemical environment within the wall rock outwardly from the vein.

Jan 1, 1947

Prof. G. W. MAYNARD, New York City (communication to the Secretary): Prof. Christy, in his admirable paper on "The Growth of American Mining Schools," has overlooked the work done by the Rensselaer Polytechnic Institute in its department of mining and metallurgy. This oversight is naturally due to the fact that the department was, for lack of money, discontinued in 1871. It was organized by the writer in 1867, starting with ten students, who had already completed the first two years of the civil engineering course in the Institute. The course covered two years, specifically devoted to mining, metallurgy and assaying, which, in connection with the two years' drill in the civil engineering department made a four years' course. During the four years of the existence of the department, thirty-five students took the course, of whom twentyfive graduated; and of this number eight have been members of the Institute of Mining Engineers, and the majority of them have occupied high positions in the profession. The equipment of the department was, at that time, second only to that of the Columbia School of Mines. As Prof. Christy has cited other institutions which are not distinctively mining schools, but in which the ruining course was subordinate to other courses, it seems to me that the work in this line carried out by the oldest engineering school in the country may very properly be referred to. In addition to the regular mining course, a special course in assaying was given; and many young men were here prepared for positions in the mines and metallurgical works of the west. PROF. George F. Swain, Boston, Mass.: I have listened with great interest to Prof. Christy's valuable paper, but there is one conclusion at which he arrives that appears to me entirely unjustifiable, and to which I desire to take exception. Prof. Christy finds that of the total wage-earners in the United States in 1880,10.41 per cent. were employed in " trade and transport;" 20.24 per cent. in " manufactures and mechanics," and 1.83

Jan 1, 1894

By John C. Calhoun, Alfred Chatenever

An exploratory study wap made to examine the possibilities of a visual approach in investigations into microscopic mechanisms of fluid behavior in porous media. Appropriate apparatus and techniques were developed so that microscopic phenomena could be recorded on color movie film as well as be observed visually. The observation flow cells in which tlie fluid behavior studies were made were essentially single-layered matrices of spheres between plates. sometimes all-glass, sometimes all-Lucite and sometimes a combination of the two. The fluids were limited to water and a filtered crude oil. Two flow regimes were observed during the flow of the immiscible liquids: channel flow and slug flow. In the former, transport was effected through stable networks of interconnecting channels; and in the latter, part of the movement took place in the form of slugs. Under certain conditions, flood-front patterns were found to be different depending upon which liquids were the displacing and displaced phases and not depending upon whether the matrix was water-wet glass or oil-wet Lucite. Residual formations of oil and water were observed and are described. Some of the ramifications and significance of the ohservetl phenomena are discussed. INTRODUCTION In recent years considerations of microscopic mechanisms of fluid flow in porous media have taken on greater significance. Much needs to be learned before the fundamentals of petroleum technology are completely established. For example, many unanswered questions exist in connection with relative permeability, displacement phenomena, residua! fluid formations. flow structure, etc.; and further analytical mathematical formulations are seriously indicated. It is hoped that systematic investigations into the microscopic mechanisms connected with the behavior of fluids in porous media will shed some light on some of the problems extant. Until recently microscopic mechanisms have been considered almost exclusively as speculative hypotheses. Within the past few years, however, the problem has been submitted to a limited number of experimental investigations. Nuss and Whiting' made some studies on the pore-space geometry of sandstones and limestones by impregnating cores with an inert plastic and leaching the solid matrices to leave behind plastic models of the pore spaces. SchaeferZ traced pore spaces microscopically through lengths of limestone cores by cutting away thin sections from the exposed faces normal to the line of view. In 1949 two projects were organized in which dynamic flow phenomena were examined microscopically to uncover microscopic mechanisms. One was set up at the Pennsylvania State College where Lowmanb bserved heterogeneous fluid flow phenomena in capillaries. The second was the American Petroleum Institute Research Project 47B at the University of Oklahoma where microscopic studies of dynamic fluid phenomena in synthetic porous matrices have been made by visual observation and cinephotomicrography.' It is with the latter that this paper is concerned. treating the techniques involved and the observations made. TECHNIQUES Observation Flow Cells The observation flow cells formed a focal point in the techniques employed. Essentially, these were matrices composed of a single layer of spheres sandwiched between two flat plates. This design was arrived at after a series of pre-

Jan 1, 1952

By C. E. Abbott

The Birmingham district, Alabama, is distinctive in the proximity to one another of its deposits of iron ore, coal and flux. These three basic requisites for the making of iron and steel are found within a radius of 10 miles. Both dolomite and limestone are produced, the former for blast-furnace flux and the latter for basic open-hearth operations. The Tennessee Coal, Iron and Railroad Co., a subsidiary of the United States Steel Corporation, operates a limestone mine at Muscoda, near Bessemer, 12 miles southwest of Birmingham, served by its own railroad transportation system. The mine has a capacity of 130 tons per hour. Average analyses of a recent month's production arc as follows: Fe²zO³ SiO² Al²O³ CaCO³ MgCO³ Lump, percent............................. 0.51 0.22 98.63 0.14 Crushed and washed, per cent,................ 0.70 0.26 98.36 0.18 Lump stone, 2 1/2 to 755 in., is used in open-hearth operations at Fairfield Steel Works. Fine crushed and washed stone, 1% to 0.063 in., is calcined at the lime-burning plant and used for lime charges at the Ensley open hearths. Geology The district's deposits of hematite ore occur in the Clinton formation, and the limestone beds mined are stratigraphically 330 ft. above the ore beds worked. A cross section on the center line of the mine is shown in Fig. 1. This limestone formation, 130 ft. thick, is in the Warsaw horizon of the Lower Mississippian. It lies above 100 ft. of Fort Payne chert, which is immediately above the Clinton formation, and is composcd of layers of chert and cherty limestone, approximately 50 per cent of the material being pure chert. The chert is extremely hard, and the cost of driving raises through it is very high. Both iron ore and limestone deposits lie on the southwest limb of the Jones Valley anticline, the formations dipping from 15' to 32' to the southeast. The iron-ore seam outcrops along the crest of Red Mountain, a ridge with northeast-southwest trend rising 200 to 300 ft. above Jones and Shades valleys at the

Jan 1, 1938

By C. E. Abbott

The Birmingham district, Alabama, is distinctive in the proximity to one another of its deposits of iron ore, coal and flux. These three basic requisites for the making of iron and steel are found within a radius of 10 miles. Both dolomite and limestone are produced, the former for blast-furnace flux and the latter for basic open-hearth operations. The Tennessee Coal, Iron and Railroad Co., a subsidiary of the United States Steel Corporation, operates a limestone mine at Muscoda, near Bessemer, 12 miles southwest of Birmingham, served by its own railroad transportation system. The mine has a capacity of 130 tons per hour. Average analyses of a recent month's production arc as follows: Fe²zO³ SiO² Al²O³ CaCO³ MgCO³ Lump, percent............................. 0.51 0.22 98.63 0.14 Crushed and washed, per cent,................ 0.70 0.26 98.36 0.18 Lump stone, 2 1/2 to 755 in., is used in open-hearth operations at Fairfield Steel Works. Fine crushed and washed stone, 1% to 0.063 in., is calcined at the lime-burning plant and used for lime charges at the Ensley open hearths. Geology The district's deposits of hematite ore occur in the Clinton formation, and the limestone beds mined are stratigraphically 330 ft. above the ore beds worked. A cross section on the center line of the mine is shown in Fig. 1. This limestone formation, 130 ft. thick, is in the Warsaw horizon of the Lower Mississippian. It lies above 100 ft. of Fort Payne chert, which is immediately above the Clinton formation, and is composcd of layers of chert and cherty limestone, approximately 50 per cent of the material being pure chert. The chert is extremely hard, and the cost of driving raises through it is very high. Both iron ore and limestone deposits lie on the southwest limb of the Jones Valley anticline, the formations dipping from 15' to 32' to the southeast. The iron-ore seam outcrops along the crest of Red Mountain, a ridge with northeast-southwest trend rising 200 to 300 ft. above Jones and Shades valleys at the

Jan 1, 1938

By W. B. Weeks, H. K. Shearer

The year 1937 brought to south Arkansas increased drilling activity and production. Oil production amounted to 12,159,440 bbl., an increase of 1,504,500 bbl., or 14.1 per cent over 1936. This was the largest production since 1931, and the first annual increase since 1925, when the deeper sands at Smackover were developed. There were 177 wells completed during the year, with 103 oil wells, 6 gas wells, and 68 dry holes, an increase of more than 100 per cent over 1936. Of the 56 wildcat wells drilled, 52 were dry and 4 produced oil. Two new fields, one important extension and three minor extensions were discovered. The trend toward deeper drilling is shown by the fact that 97 wells were more than 5000 ft. deep, including 80 over 6000 ft. and 13 over 7000 ft., although the depth record of 7973 ft., made in 1935, was not exceeded. Geological Section Deeper and more extensive drilling during the past few years, not only in south Arkansas but also in adjacent parts of north Louisiana and east Texas, has furnished much important geological information and has brought out some very unexpected facts in regard to structural and depositional conditions in the series of formations laid down in the interval between the end of the Pennsylvanian and early Cretaceous time. It is now evident that an important basin of salt deposition existed in the Arkansas-Louisiana-Texas area, but it is still an open question whether this salt basin was contemporaneous and continuous with the even larger Gulf Coast salt basin extending from Mississippi to Mexico. The accompanying columnar section (Fig. 1) shows the producing zones and names that have been applied to the several subsurface formations, most of which have no outcrop equivalents. This is for the convenience of readers unfamiliar with recent developments, but the correlations and nomenclature cannot yet be considered final. These formations will be discussed in more detail in various papers to be published in the near future.

Jan 1, 1938

Tile National Research Council announces further appointments to National Research Fellowships in physics and chemistry. The object of the National Research Council in maintaining a system of research fellowships is to promote fundamental research in physics and chemistry primarily in educational institutions in the United States. Fellowships are awarded to persons who have demonstrated a high order of ability in research for the purpose of enabling them to conduct investigations at educational institutions which make adequate provisions for research: in physics and chemistry. The new appointments are as follows: In Chemistry.-Warren C. Vosburgh, of New York City, B. S. Union College, 1914, A. M. Union College, 1916, Ph. D. Columbia University, 1919. Research assistant to the Professor of Chemistry at Columbia University for the past six months. George Scatchard, of New York City, A. B. Amherst College, 1913, Ph. D. Colt tibia University, 1917. Formerly research assistant to the Professor of Chemistry at Columbia University and instructor in organic chemistry: First Lieutenant. Sanitary Corns. U. S. A.

Jan 7, 1919

By G. M. Schwartz, J. N. Gundersen

Utilization of magnetite-bearing taconite from the great Mesabi range of Minnesota is fast becoming a major industry in the state. The planning and early development stages of taconite processing projects have been de-scribed1-3 and an excellent discussion has appeared recently4 concerning the current mining, crushing, concentrating, and pelletizing techniques of the Reserve Mining Co., whose operations lie entirely within the Eastern Mesabi district. The present paper will deal only with some of the geological aspects of taconite utilization in the district, with emphasis placed upon some of the common mineralogical and textural features of the tacon-ites currently being mined or stripped and how these factors generally affect the potential recovery of the iron from the metamorphosed Biwabik iron-formation. The generalized geologic setting of the Eastern Mesabi district is presented in Fig. 1. The small circles on the geologic map, adapted from Grout and Broderick,3 mark the location of drill holes that were available for inspection during this study through the courtesy of Reserve Mining and Erie Mining Cos. The cores from these holes were divided into stratigraphic units and examined for their mineral content. Typical mineral associations and grain fabrics were also determined from hundreds of thin and polished sections. Available metallurgical tests made it possible to determine the probable response of a given variety of taconite to magnetic concentration. The longitudinal section of Fig. 1, projected along the strike of the iron formation, presents the simple stratigraphy of the area. It also shows the uniformly thick nature of the iron formation members in the district as well as a somewhat abrupt thickening of the formation to the west of the probable fault. The stratigraphy of these precambrian rocks has been described5-' elsewhere and need only be briefly reviewed. Historically, the oldest rocks unit, the Giants Range granite (Algoman) was covered by the Animikie group of sediments (Middle Huronian?), consisting of the Pokegama, Biwabik, and Virginia formations. Outcrops of the Pokegama quartzite are locally distributed along the northern limit of the Biwabik iron formation, but they are too limited to depict on the geologic map of Fig. 1. The effects of the intrusion of several small diabase sills within the Virginia and Biwabik formations are obscure because all of these rocks have been subsequently highly metamorphosed, mainly by the Duluth gabbro. The emplacement of the transgressing Duluth gabbro (Middle Keweenawan) and that of numerous peg-matitic veins in the iron formation8 has resulted in extensive contact and metasomatic metamorphism which has locally reconstituted the previously existing minerals of the Biwabik formation, in large part quartz and magnetite, into a wide variety of silicate mineral assemblages9 that have a profound effect upon the re coverability of the remaining magnetite. The entire region has subsequently been eroded and largely buried beneath Pleistocene glacial deposits. Structurally, the strike of the gently dipping Animikie group generally parallels the elongate outcrop pattern of the Biwabik iron formation on the map of Fig. 1. The Animikie group most commonly dips from 5" to 15" to the south-southeast. In this area, the Duluth gabbro pluton is somewhat sill-like, dipping about 30" to the southeast. Projecting these present structures upward, it seems probable that the gabbro once extended over the underlying Animikie group in the Eastern Mesabi district. SELECTION AND PRESENTATION OF DATA Because of the locally intense metamorphic activity in the district, mineralogical variations within the magnetite-bearing taconites are commonly abrupt, both vertically and laterally. Consequently it is difficult to select a single hole or small group of holes whose cores will be entirely representative of all of the district. Two holes have been selected, however, that in a general way represent mineralogical and textural variations that are likely to be encountered in both the eastern and western parts of the district. These recently drilled holes were chosen for discussion because it was possible to log the core and then to place the sample intervals at stratigraphic boundaries prior to preparation of the core for magnetic tube tests.

Jan 1, 1961

By Samuel M. Brock

Problems related to strip and auger coal mining have grown with the development of the industry and the economy. New technology has produced equipment that has made mining by surface methods not only highly productive, but potentially highly destructive of water resources and natural environments. On the other hand, growth of the economy has produced an increased demand for clean water and created new demands for amenity values that natural environments provide. Thus, opposing forces have created conflicts in resource use. And these conflicts have made surface mining highly controversial. Resolving the controversy will require the solving of complex economic and social problems. The essence of the economic problem created by surface mining is that, in the absence of proper regulation, substantial costs resulting from the process are borne by the public rather than the mine operator. The major goal for the regulation of the surface mining industry is to provide controls which will promote the attainment of maximum social welfare. Deciding upon the type of controls required, and how to apply them to attain a social optimum, however, poses some very difficult problems. In a comprehensive article on this subject, David B. Brooks defined the problem and suggested that benefit- cost analysis might be helpful in providing guidelines for making decisions about surface mining regulations.1

Jan 5, 1969

By Y. L. Yao

The solubility limit of oxygeu in a titanionn at 850°C has been determined by magnetic measurements as 12.5 + 0.5 pct (29.0—30,9 at. pct). Also in the susceptibility-co~centmtion curve, there is n distinct but not sharp maximum at 19.0 * 0.5 z~t pet (40.5--42.1 at. pct), which indicates the presence of the 6 phase. The magnetic susceptibilities of the alloys of the titanium-oxygen system were determined byEhrlich in 1939.' is alloys were prepared by sintiring mixtures of titanium and its oxide at high temperatures. On the titanium-rich side, despite the fact that the alloy compositions he measured crossed two phase boundaries, the limited results obtained

Jan 1, 1960

By R. W. Shoenberger, J. E. McNulty, B. R. Kuchta, William Spackman, A. A. Terchick, M. E. Hopkins, Norman Schapiro, R. J. Gray, A. F. Duzy, M. P. Corriveau

INTRODUCTION * The United States is fortunate in having abundant reserves of metallurgical-grade coals. Although these coals are better in quality and more accessible than most metallurgical-grade coals found throughout the rest of the world, the best grades of these coals are being depleted. Consequently, more efficient exploration tools and techniques, such as advanced methods of core drilling and logging, correlation by petrography, paleontology, palynology, † physical stratigraphy, and geophysical methods are being used to help assess the extent and quality of the remaining coal reserves. Exploration and assessment of new and existing coal properties become of utmost importance in determining ( 1 ) the economic justification for mining the coal, (2) the optimum design of the preparation plant, and (3) the most effective use of the coal. Recent progress has been made in relating mineral matter, especially pyrite, in coal to geologic conditions and paleogeographic trends. l * Editor's note: Because of the numerous and varied contributions of the associate authors of this chapter, the text does not differentiate between sections prepared by each individual as has been done in other chapters. † Palynology is the science concerned with plant microfossils, especially spores. pollen. and other fossils of microscopic size.

Jan 1, 1979

By Maynard H. Jameson

Earlier investigations of the potential-drop-ratio method of electrical prospecting have indicated that under suitable conditions this method is well adapted to the location of formation boundaries in stratified ground. A description of this development was given several years ago by H. Lundberg and Th. Zuschlag.l The curves published by these authors for the potential-drop-ratio variation above a horizontal contact indicated a definite relation of the position of the curve peak to the depth of the interface. The theory underlying this relation was subsequently studied by Z. Mitera in greater detail,' and the theoretical deductions were compared with the results of tank experiments. The investigations available at this writing were confined to studies of horizontal formation boundaries. It is the purpose of this paper to extend the scope of the previous work to the problem of dipping layers. Theory Consider the case of three media of different resistivities, whose interfaces are not parallel. If a point-source is located in one of these interfaces, its images do not lie in a straight line, but on the circumference of a circle whose center is at the hypothetical junction of the interfaces. R. F. Aldredgea determined the relation that exists between the degrees of dip of the two interfaces and the distances between the various images and the point for which the potential is to be found. As seen in Fig. I, three media of resistivities PO, p1, and p2 are involved, and the source I is located at the interface of the media Coo) and (p1). The perpendicular depth of the lower interface is h, 0 is the dip, R is the distance between source I and potential point P, and r is the distance between the images and that point. To distinguish between images lying above the ground interface and those below, the notation "odd" and "even" images will be employed; images below the ground interface will be termed "odd" and those above "even." The following relations govern the distances between either kind of images and the potential point: EvEn Odd Ta — R r1 - [rl] - [RS + 4h(h + R sin 01½ r, = [r] =. [R1 + 4h cos 0)2(h + -R sin 0)1½ ri - [r3] ={r3} [R* + 4h(4 cos2 0 - i)1 (h + R sin 0)l½ r4 = [r4] = [R2 + 4h(4 cos $ cos 30)1 (h + R sin 0)]½ r, — [r4] - [R2 + 4h(4 cos9 R cos 20 + cos 48)2 (h + R sin 01½ I RI + 4h[2 cos 30(4 cos2 0 - I)12 (h + R sin 8)1 ½ rn - [r4] - [R2 + 4hlf(cOs 0)18(h + R sin R)l½ As previously pointed out, the images of the source are on the circumference of a circle. If the angle of dip is 0, the angle measured from the horizontal to the first image is 28; to the second image it is 48, and so on. Since the limit of the reflecting interface is at its outcrop, the last possible

Jan 1, 1946

By Maynard H. Jameson

Earlier investigations of the potential-drop-ratio method of electrical prospecting have indicated that under suitable conditions this method is well adapted to the location of formation boundaries in stratified ground. A description of this development was given several years ago by H. Lundberg and Th. Zuschlag.l The curves published by these authors for the potential-drop-ratio variation above a horizontal contact indicated a definite relation of the position of the curve peak to the depth of the interface. The theory underlying this relation was subsequently studied by Z. Mitera in greater detail,' and the theoretical deductions were compared with the results of tank experiments. The investigations available at this writing were confined to studies of horizontal formation boundaries. It is the purpose of this paper to extend the scope of the previous work to the problem of dipping layers. Theory Consider the case of three media of different resistivities, whose interfaces are not parallel. If a point-source is located in one of these interfaces, its images do not lie in a straight line, but on the circumference of a circle whose center is at the hypothetical junction of the interfaces. R. F. Aldredgea determined the relation that exists between the degrees of dip of the two interfaces and the distances between the various images and the point for which the potential is to be found. As seen in Fig. I, three media of resistivities PO, p1, and p2 are involved, and the source I is located at the interface of the media Coo) and (p1). The perpendicular depth of the lower interface is h, 0 is the dip, R is the distance between source I and potential point P, and r is the distance between the images and that point. To distinguish between images lying above the ground interface and those below, the notation "odd" and "even" images will be employed; images below the ground interface will be termed "odd" and those above "even." The following relations govern the distances between either kind of images and the potential point: EvEn Odd Ta — R r1 - [rl] - [RS + 4h(h + R sin 01½ r, = [r] =. [R1 + 4h cos 0)2(h + -R sin 0)1½ ri - [r3] ={r3} [R* + 4h(4 cos2 0 - i)1 (h + R sin 0)l½ r4 = [r4] = [R2 + 4h(4 cos $ cos 30)1 (h + R sin 0)]½ r, — [r4] - [R2 + 4h(4 cos9 R cos 20 + cos 48)2 (h + R sin 01½ I RI + 4h[2 cos 30(4 cos2 0 - I)12 (h + R sin 8)1 ½ rn - [r4] - [R2 + 4hlf(cOs 0)18(h + R sin R)l½ As previously pointed out, the images of the source are on the circumference of a circle. If the angle of dip is 0, the angle measured from the horizontal to the first image is 28; to the second image it is 48, and so on. Since the limit of the reflecting interface is at its outcrop, the last possible

Jan 1, 1946

By William E. Ford, Edward Salisbury Dana

The Silicates are m part strictly anhydrous, in part hydrous, as the zeolites and the amorphous clays, etc. Furthermore, a large number of the silicates yield more or less water upon ignition, and in many cases it is known that they are, therefore, to be regarded as basic (or acid) silicates. The line, however, between the strictly anhydrous and hydrous silicates cannot be sharply drawn, since with many species which yield water upon ignition the part played by the elements forming the water is as yet uncertain. Furthermore, in the cases of several groups, the strict arrangement must be deviated from, since the relation of the species is best exhibited by introducing the related hydrous species immediately after the others. This chapter closes with a section including the Titanates, Silico-titanates, Titano-niobates, etc., which connect the Silicates with the Niobates and Tantalates. Some Titanates have already been included among the Oxides.

Jan 1, 1922

Truman H. Aldrich '78 Andrew S. McCreath '75 W. S. Ayres '73 Walter McDermott '74 A. A. Blair '75 Philip N. Moore '74 Walter M. Brodie '72 Henry S. Munroe '72 H. M. Chance '74 James Wilson Neill '79 Frederick G. Corning '77 I. P. Pardee '73 Henry S. Drinker Founder Edward C. Potter '79 Ernest F. Eurich '74 Alexandre Pourcel '77 W. E. C. Eustis '76 William H. Radford '76 A. Heckscher '79 Robert H. Richards '75 Henry D. Hibbard '79 Albert F. Schneider '74 Julian Kennedy '79 Porter W. Shimer '79 William St. George Kent '72 John Stevenson, Jr '76 Frank Lyman '77 Arthur Thacher '76 John Markle '79 Edward H. Williams '76 Samuel Mather '79 Thomas D. Wood '79

Jan 1, 1929

By F. B. Foley

A description of tests made by a committee of the Division of Engineering of the National Research Council to determine whether velocity of impact affects the formation of Neumann bands. FOREWORD Not infrequently, in the case of the failure of a metal structure, such as a bridge, tank, airplane, gun carriage, etc., a doubt arises whether the failure was due, among other causes, to the effect of an overburden or of an explosive maliciously or accidentally exploded in contact with it. As few means of discriminating between the effects of these causes have been known and these means were of a rough qualitative character, it was surprising to find in the record of an inquiry into the failure of a structure, the statement that, by observations on the Neumann bands in the structure, it was possible to determine the speed of breakage in the metal and to distinguish between a fracture caused by an explosion and one caused by an ordinary mechanical strain. Such a criterion, if well proved, was of value to the explosives experts of the Bureau of Mines, the Ordnance Department of the United States Army and the Bureau of Ordnance of the United States Navy, but search showed no record of it in the literature nor did any of the metallurgists and metallographers consulted know of any data on which such a criterion could be based having been assembled and critically studied. However, it was universally held that there was promise in the idea and that there existed unique facilities at the Bureau of Mines Experiment Station at Pittsburgh for the preparation, under definitely known conditions, of material for study by metal-lographers, and that material of value might also be obtained from the proving grounds of the Army and Navy. Therefore, with the approval of the Director of the Bureau of Mines and the Chiefs of Ordnance of the War and Navy Departments, the Chairman of the Division of Engineering of the National Research Council, on April 12, 1919, appointed a Committee on the Investigation of Neumann Bands, which has since been engaged in this study and which, after some slight change in its personnel, consists now of the following: Dr. William Campbell, Advisory Metallurgist, Bureau of Ordnance, Navy Department. F. B. Foley, Metallurgist, Bureau of Mines. S P. Howell, Explosives Engineer, Bureau of Mines. Comdr. O. M. Hustvedt, U. S. N., Bureau of Ordnance, Navy Department. Dr. Charles E. Munroe, Chief Explosives Chemist, Bureau of Mines.

Jan 9, 1922